137 lines
3.8 KiB
Matlab
137 lines
3.8 KiB
Matlab
% converErrorBasis
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% :PROPERTIES:
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% :header-args:matlab+: :tangle src/converErrorBasis.m
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% :header-args:matlab+: :comments org :mkdirp yes
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% :header-args:matlab+: :eval no :results none
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% :END:
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% <<sec:converErrorBasis>>
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% This Matlab function is accessible [[file:src/converErrorBasis.m][here]].
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function error_nass = convertErrorBasis(pos, setpoint, ty, ry, rz)
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% convertErrorBasis -
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%
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% Syntax: convertErrorBasis(p_error, ty, ry, rz)
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%
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% Inputs:
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% - p_error - Position error of the sample w.r.t. the granite [m, rad]
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% - ty - Measured translation of the Ty stage [m]
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% - ry - Measured rotation of the Ry stage [rad]
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% - rz - Measured rotation of the Rz stage [rad]
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%
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% Outputs:
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% - P_nass - Position error of the sample w.r.t. the NASS base [m]
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% - R_nass - Rotation error of the sample w.r.t. the NASS base [rad]
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%
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% Example:
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%
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%% If line vector => column vector
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if size(pos, 2) == 6
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pos = pos';
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end
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if size(setpoint, 2) == 6
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setpoint = setpoint';
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end
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%% Position of the sample in the frame fixed to the Granite
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P_granite = [pos(1:3); 1]; % Position [m]
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R_granite = [setpoint(1:3); 1]; % Reference [m]
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%% Transformation matrices of the stages
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% T-y
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TMty = [1 0 0 0 ;
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0 1 0 ty ;
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0 0 1 0 ;
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0 0 0 1 ];
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% R-y
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TMry = [ cos(ry) 0 sin(ry) 0 ;
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0 1 0 0 ;
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-sin(ry) 0 cos(ry) 0 ;
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0 0 0 1 ];
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% R-z
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TMrz = [cos(rz) -sin(rz) 0 0 ;
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sin(rz) cos(rz) 0 0 ;
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0 0 1 0 ;
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0 0 0 1 ];
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%% Compute Point coordinates in the new reference fixed to the NASS base
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% P_nass = TMrz*TMry*TMty*P_granite;
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P_nass = TMrz\TMry\TMty\P_granite;
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R_nass = TMrz\TMry\TMty\R_granite;
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dx = R_nass(1)-P_nass(1);
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dy = R_nass(2)-P_nass(2);
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dz = R_nass(3)-P_nass(3);
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%% Compute new basis vectors linked to the NASS base
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% ux_nass = TMrz*TMry*TMty*[1; 0; 0; 0];
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% ux_nass = ux_nass(1:3);
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% uy_nass = TMrz*TMry*TMty*[0; 1; 0; 0];
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% uy_nass = uy_nass(1:3);
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% uz_nass = TMrz*TMry*TMty*[0; 0; 1; 0];
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% uz_nass = uz_nass(1:3);
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ux_nass = TMrz\TMry\TMty\[1; 0; 0; 0];
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ux_nass = ux_nass(1:3);
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uy_nass = TMrz\TMry\TMty\[0; 1; 0; 0];
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uy_nass = uy_nass(1:3);
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uz_nass = TMrz\TMry\TMty\[0; 0; 1; 0];
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uz_nass = uz_nass(1:3);
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%% Rotations error w.r.t. granite Frame
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% Rotations error w.r.t. granite Frame
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rx_nass = pos(4);
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ry_nass = pos(5);
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rz_nass = pos(6);
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% Rotation matrices of the Sample w.r.t. the Granite
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Mrx_error = [1 0 0 ;
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0 cos(-rx_nass) -sin(-rx_nass) ;
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0 sin(-rx_nass) cos(-rx_nass)];
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Mry_error = [ cos(-ry_nass) 0 sin(-ry_nass) ;
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0 1 0 ;
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-sin(-ry_nass) 0 cos(-ry_nass)];
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Mrz_error = [cos(-rz_nass) -sin(-rz_nass) 0 ;
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sin(-rz_nass) cos(-rz_nass) 0 ;
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0 0 1];
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% Rotation matrix of the Sample w.r.t. the Granite
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Mr_error = Mrz_error*Mry_error*Mrx_error;
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%% Use matrix to solve
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R = Mr_error/[ux_nass, uy_nass, uz_nass]; % Rotation matrix from NASS base to Sample
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[thetax, thetay, thetaz] = RM2angle(R);
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error_nass = [dx; dy; dz; thetax; thetay; thetaz];
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%% Custom Functions
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function [thetax, thetay, thetaz] = RM2angle(R)
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if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
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thetay = -asin(R(3, 1));
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% thetaybis = pi-thetay;
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thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
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% thetaxbis = atan2(R(3, 2)/cos(thetaybis), R(3, 3)/cos(thetaybis));
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thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
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% thetazbis = atan2(R(2, 1)/cos(thetaybis), R(1, 1)/cos(thetaybis));
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else
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thetaz = 0;
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if abs(R(3, 1)+1) < 1e-6 % R31 = -1
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thetay = pi/2;
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thetax = thetaz + atan2(R(1, 2), R(1, 3));
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else
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thetay = -pi/2;
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thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
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end
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end
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end
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end
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